CALT Revised October Interval Estimation using the Likelihood Function

The general properties of two commonly used methods of interval estimation for population parameters in physics are examined Both of these methods em ploy the likelihood function i Obtaining an interval by nding the points where the likelihood decreases from its maximum by some speci ed ratio ii Obtaining an interval by nding points corresponding to some speci ed fraction of the total integral of the likelihood function In particular the conditions for which these methods give a con dence interval are illuminated following an elaboration on the de nition of a con dence interval The rst method in its general form gives a con dence interval when the parameter is a function of a location parameter The second method gives a con dence interval when the parameter is a location param eter A potential pitfall of performing a likelihood analysis without understanding the underlying probability distribution is discussed using an example with a normal likelihood function The connection with Bayesian statistics is also noted Somewhat expanded version of publication in Nucl Inst Meth A Work supported in part by the Department of Energy grant DE FG ER